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Warm up

Warm up.

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Warm up

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  1. Warm up • The Pendleton County School District is trying to decide on a new copier. The purchasing committee has been given quotes on two new machines. One sells for $20,000 and costs $0.02 per copy to operate. The other sells for $17,500, but its operating cost is $0.025 per copy. The district estimates the number of copies made each year is 515,000. Based on this estimation, which machine would you recommend? Justify your choice with clear mathematics.

  2. Answer • The operating costs can be determined using equations for each copier. Let C represent the operating cost and p represent the number of pages copied. • Copier 1: C = 20,000 + 0.02p • Copier 2: C = 17,500 + 0.025p • Copier 1: C = 20,000 + 0.02(515,000) = 30,300 • Copier 2: C = 17,500 + 0.025(515,000) = 30,375 • Copier 1 costs $30,300 for 515,000 copies. • Copier 2 costs $30,375 for 515,000 copies. • Copier 1 would be the best copier for this district because it is cheaper at the estimated number of pages.

  3. Warm-Up Distributive Property of Equality 24 = 2x Division Property of Equality Symmetric Property of Equality

  4. Questions over hw? Elimination Practice

  5. CCGPS Coordinate AlgebraDay 19 (9-7-12) UNIT QUESTION: How do I justify and solve the solution to a system of equations or inequalities? Standard: MCC9-12.A.REI.1, 3, 5, 6, and 12 Today’s Question: When is it better to use substitution than elimination for solving systems? Standard: MCC9-12.A.REI.6

  6. Solve Systems of Equations by Graphing

  7. Steps to Graphing • Make sure each equation is in slope-intercept form: y = mx + b. • Graph each equation on the same graph paper. • The point where the lines intersect is the solution. If they don’t intersect then there’s no solution. • Check your solution algebraically.

  8. 1. Graph to find the solution. Solution: (-1, 3)

  9. 2. Graph to find the solution. No Solution

  10. 3. Graph to find the solution. Solution: (-3, 1)

  11. 4. Graph to find the solution. Solution: (-2, 5)

  12. 3 Types of Systems

  13. So basically…. • If the lines have the same y-intercept b, and the same slope m, then the system is consistent-dependent. • If the lines have the same slope m, but different y-intercepts b, the system is inconsistent. • If the lines have different slopes m, the system is consistent-independent.

  14. Solve Systems of Equations by Substitution

  15. Steps for Substitution • One equation will have either x or y by itself, or can be solved for x or y easily. • Substitute the expression from Step 1 into the other equation and solve for the other variable. • Substitute the value from Step 2 into the equation from Step 1 and solve. • Your solution is the ordered pair formed by x & y. • Check the solution in each of the original equations.

  16. Solve by Substitution 1. x = -4 3x + 2y = 20 1. (-4, 16)

  17. Solve by Substitution 2. y = x - 1 x + y = 3 2. (2, 1)

  18. Solve by Substitution 3. 3x + 2y = -12 y = x - 1 3. (-2, -3)

  19. Solve by Substitution 4. x = 1/2 y - 3 4x - y = 10 4. (8, 22)

  20. Solve by Substitution 5. x = -5y + 4 3x + 15y = -1 5. No solution

  21. Solve by Substitution 6. 2x - 5y = 29 x = -4y + 8 6. (12, -1)

  22. Solve by Substitution 7. x = 5y + 10 2x - 10y = 20 7. Many solutions

  23. Solve by Substitution 8. 2x - 3y = -24 x + 6y = 18 9. (-6, 4)

  24. CW/HW

  25. HW Graphing and Substitution WS

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